Students can develop a strong understanding of measurement and measurement systems from consistent experiences in classroom activities where a variety of manipulatives and technology are used. The key components of this understanding, as identified in the K12 Overview, are: the concept of a measurement unit; standard measurement units; connections to other mathematical areas and to other disciplines; indirect measurement; and, for older students, measurement error and degree of precision.

Students in the early grades encounter measurement in many situations, from their daily work with the calendar, to situations in stories that they are reading, to describing how quickly they are growing. Hands-on science activities often require students to measure objects or compare them directly. Daily calendar activities frequently offer work with temperature, time, and money, in addition to number. Thus, many opportunities for connections present themselves in a natural way.

The study of measurement also encourages students to develop their number sense and to practice their counting skills. By using measures, students can recognize that numbers are often used to describe and compare properties of physical objects. Students in the early grades should make estimates not only of discrete objects like marbles or seeds but also of continuous properties like the length of a jumprope or the number of children's feet which might fit in a dinosaur's footprint.

Students need to focus on identifying the property that they wish to measure. They should understand what is meant by the length of an object or its weight or its capacity. Concrete experiences in describing the properties of objects, in sorting objects, and in comparing and contrasting objects provide them with opportunities to develop these concepts.

Students begin by making direct comparisons. Which string is longer? Which child is taller? Which rock is heavier? Which glass holds more? Making comparisons will help children better to understand the properties which they are discussing. They also begin to make some indirect measurements. For example, in order to compare the height of the blackboard with the height of a window, they might measure both objects using links and then compare the number of links used for each. In this way, they start to see a need for a measurement unit, a unit that they can use over and over to compare to a variety of objects.

In grades K-2, students should use a variety of non-standard units to measure objects. How many links long is a desk? How many erasers high are you? How many pennies balance a Unifix cube? In each case, students should first be asked to make an estimate and then proceed to actually measure the object. Students should also use different units to measure the same object. They should begin to understand that when the size of a measuring unit increases, the number of units needed to measure the object decreases.

In these grades, students also begin to use standard measurement units and standard measurement devices such as rulers and scales. It is important that the students see the use of the standard devices as simply an extension of their earlier activities. For example, the use of an inch ruler is just a more efficientprocedure than lining up a series of cubic inch blocks. Students should explore length using inches, feet, centimeters and meters; liquid capacity using quarts, pints, cups, and liters; mass/weight using pounds, ounces, grams, and kilograms; time using days, weeks, months, years, seconds, minutes, and hours; and temperature using degrees Fahrenheit and Celsius.

Whether making direct comparisons, using non-standard units, or using standard measurement units, students in the early grades should always estimate a measure first and then perform the measurement. In this way, their estimation and number sense skills will be reinforced.

The cumulative progress indicators for grade 4 appear below in boldface type. Each indicator is followed by activities which illustrate how it can be addressed in the classroom in kindergarten and grades 1 and 2.

Experiences will be such that all students in grades K-2:

1. Use and describe measures of length, distance, capacity, weight, area, volume, time, and temperature.

• Students find out how many cubes long their hand is. The class can then generate a graph showing the results.

• Using a large map of the school community, students estimate and then use paper clips or links to measure who lives farthest from school. This type of activity might be related to a specific story that was used in the Social Studies unit on community.

• Students name objects big enough to hold a football or too small to hold a soccer ball.

• Students lay out a model zoo with several toy animals, using boxes of different sizes for their cages or yards. They also cut doors of appropriate sizes in the boxes for the animals.

• Students listen to and look at the book Let's Find Out about What's Light and What's Heavy by Martha and Charles Shapp. The simple text and humorous illustrations lead to the conclusion that weighing things using a standard unit of weight helps answer the question in the title.

• Students name objects they can lift and ones that they cannot lift.

• Students estimate and then use balances to find out how many pennies balance a small familiar object.

• Students cut strips of paper to fit around a pumpkin or to make Santa's belt.

• Students fill a large bottle with water using first a 4 ounce cup and then an 8 ounce cup. They then compare the results.

• Students make their own measuring jug using a large plastic jar. They pour in one cupful of water and mark the water level on the jar with a marker; they repeat this procedure with one cupful after another until no further cupfuls will fit inside the jar.

• Students read The Little Gingerbread Man and make a gingerbread village. In doing so, they measure lengths and capacities.

• Students make their own paper clip ruler. First they make a paper clip chain and then paste it down on a long cardboard strip. They draw a small vertical line where each paper clip ends.

• Students estimate and measure the distance around an object using Unifix cubes or a paper clip chain.

• Students conduct experiments using timers: How many times can you bounce a ball before all the water runs out of the can? How many times can you clap your hands before the sand runs out of the timer? How many times can you blink your eyes before the second hand goes all the way around the clock?

• Students read or listen to The Very Hungry Caterpillar by Eric Carle which shows the time of day at which various activities occur.

• Students make a book describing their day at school. On each page, they stamp a clock face and write underneath a time that the teacher has written on the board. They then draw the hands on the face to show the time. When the actual time of day on the classroom clock matches a time in their book, students draw a picture of what they are doing next to the correct clock face.

• Students line up Cuisenaire Rods in different combinations to measure the width of a sheet of paper.

2. Compare and order objects according to some measurable attribute.

• Kindergarten students listen to and look at the book Big Friend, Little Friend by Eloise Greenfield. In it a young boy and his two friends explore situations that clearly demonstrate what it means to be big and what it means to be little. As a nice followup assessment activity to this and other manipulative activities, the teacher has the students draw pictures which illustrate "big and little."

• Students compare the lengths of pencils to find out which is longest. They arrange a set of pencils in order from longest to shortest.

• Students use water, rice, or sand to fill different objects, pouring from one object into another to find out which object holds more. They explain how the shape of each object plays a role in the amount it holds.

• Students line up in order, from tallest to shortest.

• Children make stick drawings of a family: father, mother, school-aged child, and baby. They discuss which stick drawings are taller or shorter than others, and relate these to the relative size of the individuals in the family.

• Students collect a large variety of cardboard boxes and arrange them in order from smallest to largest.

• Each group of students is given a cup and several containers of different sizes, plain white paper, some uncooked rice, and 1 inch graph paper. They find out how many cups of rice will fit in each container and show the number of cups as a bar on the graph paper under a picture of the container. After completing the graph, they arrange the containers in order from largest to smallest.

• Students work through the Will a Dinosaur Fit? lesson that is described in the First Four Standards of this Framework. They arrange the dinosaurs in order from tallest to smallest according to their height, and from longest to shortest according to their length.

3. Recognize the need for a uniform unit of measure.

• Students measure the width of their desks by counting how many widths of their hands it would take to go from one end of the desk to the other. They compare their results and discuss what would happen to the number of hands if the teacher's hand were used instead.

• Students read and discuss How Big Is a Foot? by Rolf Myllar. The king wishes to give the queen a special bed for her birthday and measures the size using his own foot. He gives the measurements to the carpenter, who gives them to the little apprentice. The bed that he makes is too small, but the apprentice solves the problem and everyone lives happily ever after. The students use their own feet to measure the width or length of the hallway and compare their results. Finally, they measure the hallway using meter sticks.

• As an assessment of the students' understanding of units, the teacher has the students measure the length of their math book using paper clips, unifix cubes, and yellow Cuisenaire Rods. They write about their results and explain why they are different.

4. Develop and use personal referents for standard units of measure (such as the width of a finger to approximate a centimeter).

• Students identify parts of their body that are the same length as the unit cube from a base tens block set (1 centimeter).

• Students make a list of foods or drinks that come in quarts and others that come in liters.

• Students find out that ten pennies weigh about an ounce.

• Students find that first-graders are a little taller or a little shorter than a meter.

5. Select and use appropriate standard and non-standard units of measurement to solve real-life problems.

• Students decide whether they should use paper clips or pennies to measure the weight of a pencil.

• Students discuss whether they should use links or meter sticks to measure the length of the gym.

• Students write about how they might measure the distance from the cafeteria to their classroom.

6. Understand and incorporate estimation and repeated measures in measurement activities.

• Students estimate how many of their shoes will fit in a giant's footprint (left conveniently on the classroom blackboard!) and write their estimates. They trace around their shoes and cut out the tracings. After the teacher has pasted a few shoes onto the giant's footprint, the students revise their estimate. They then check the accuracy of their estimates by pasting as many shoes as will fit into the footprint.

• Students estimate the weight of various objects in beans and then use a balance scale to check the accuracy of their measurements.

References

Carle, Eric. The Very Hungry Caterpillar. New York: Philomel Books, 1987.

Greenfield, Eloise. Big Friend, Little Friend. New York: Black Butterfly Children's Books, 1991.

Myllar, Rolf. How Big is a Foot? New York: Dell Publishing, 1962.

Shapp, Martha, and Charles Shapp. Let's Find Out about What's Light and What's Heavy. New York: Franklin Watts, 1975.

General reference

Burton, G., and T. Coburn. Curriculum and Evaluation Standards for School Mathematics: Addenda Series: Kindergarten Book. Reston, VA: National Council of Teachers of Mathematics, 1991.

One-Line Resources

http://dimacs.rutgers.edu/archive/nj_math_coalition/framework.html/

The Framework will be available at this site during Spring 1997. In time, we hope to post additional resources relating to this standard, such as grade-specific activities submitted by New Jersey teachers, and to provide a forum to discuss the Mathematics Standards.